(Now, I believe this woman probably needed to examine exactly why no man she had dated in her entire life wanted a child with her, or, alternately, why she rejected every man she dated as worthy of being a father, but we're not really here to discuss her).
Just on no man wanting a child with her, it is reported that she and the husband were trying (unsuccessfully) for a child.
And as to her 'rejecting every man', she had, apparently, deemed the lover a suitable, even 1st preference, partner/father, but presumably he didn't reciprocate (did not leave his wife for her and the baby, and has not as far as we know come to be with her and the child following his own subsequent divorce).
We don't know, but my guess is he (the lover) probably knew the baby was his, and he surely must know now. First, she may have told him during the affair that she and the husband could not conceive, and second, according to reports of what his later ex-wife told the cuckolded husband, she wanted him (the lover) to be with her, so letting him know who the biological father was (she herself apparently knew) would make more sense than concealing it from him. Or he may have guessed, either just from general circumstances or from seeing some resemblances in the child. I wonder how the conception happened? But that's something we don't know. The woman may not have had a deliberate, conscious plan in that regard. We can only speculate, but if the husband is in his 40's, and she a similar age, and they had not previously had a child, it was getting to the point where if they wanted one, then regardless of the psychologies and motivations involved, the clock was ticking.
I wonder whether the wife's lover and his own wife had any children themselves, and where they are now, after that divorce? It's possible she divorced him, having found out in 2016 about the affair and the paternity of the child here.
Messy stuff.